{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9fb424d6",
   "metadata": {},
   "source": [
    "# 贝塞尔曲线的解析表达式\n",
    "\n",
    "## 定义\n",
    "贝塞尔曲线(Bézier curve)是一种参数化曲线，由一组控制点定义。给定n+1个控制点P₀, P₁, ..., Pₙ，n阶贝塞尔曲线的解析表达式为：\n",
    "\n",
    "## 一般形式\n",
    "对于t ∈ [0,1]，贝塞尔曲线B(t)的表达式为：\n",
    "\n",
    "$$\n",
    "B(t) = \\sum_{i=0}^{n} \\binom{n}{i} (1-t)^{n-i} t^i P_i\n",
    "$$\n",
    "\n",
    "其中：\n",
    "- $\\binom{n}{i}$是二项式系数（组合数）\n",
    "- $P_i$是第i个控制点\n",
    "- $t$是参数，取值范围[0,1]\n",
    "\n",
    "## 常见低阶贝塞尔曲线\n",
    "\n",
    "### 线性贝塞尔曲线（1阶，2个控制点）\n",
    "$$\n",
    "B(t) = (1-t)P_0 + tP_1\n",
    "$$\n",
    "\n",
    "### 二次贝塞尔曲线（2阶，3个控制点）\n",
    "$$\n",
    "B(t) = (1-t)^2P_0 + 2(1-t)tP_1 + t^2P_2\n",
    "$$\n",
    "\n",
    "### 三次贝塞尔曲线（3阶，4个控制点）\n",
    "$$\n",
    "B(t) = (1-t)^3P_0 + 3(1-t)^2tP_1 + 3(1-t)t^2P_2 + t^3P_3\n",
    "$$\n",
    "\n",
    "## 矩阵表示（以三次贝塞尔曲线为例）\n",
    "三次贝塞尔曲线也可以用矩阵形式表示：\n",
    "\n",
    "$$\n",
    "B(t) = \\begin{bmatrix} t^3 & t^2 & t & 1 \\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "-1 & 3 & -3 & 1 \\\\\n",
    "3 & -6 & 3 & 0 \\\\\n",
    "-3 & 3 & 0 & 0 \\\\\n",
    "1 & 0 & 0 & 0\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "P_0 \\\\ P_1 \\\\ P_2 \\\\ P_3\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "## 性质\n",
    "1. **端点插值性**：曲线总是通过第一个和最后一个控制点（P₀和Pₙ）\n",
    "2. **凸包性**：曲线完全位于控制点的凸包内\n",
    "3. **仿射不变性**：对曲线进行仿射变换等价于对控制点进行仿射变换\n",
    "4. **递推关系**：可以用德卡斯特里奥(de Casteljau)算法递归计算\n",
    "\n",
    "## 导数\n",
    "贝塞尔曲线的导数是另一个低一阶的贝塞尔曲线：\n",
    "\n",
    "$$\n",
    "B'(t) = n \\sum_{i=0}^{n-1} \\binom{n-1}{i} (1-t)^{n-1-i} t^i (P_{i+1} - P_i)\n",
    "$$\n",
    "\n",
    "这个性质在计算曲线切线和曲率时非常有用。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c4a5e3ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import PathPatch\n",
    "from matplotlib.path import Path\n",
    "import math\n",
    "\n",
    "# 解决中文乱码问题\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei'] # 设置字体为黑体\n",
    "plt.rcParams['axes.unicode_minus'] = False # 解决负号显示为方块的问题\n",
    "\n",
    "def bezier_curve(points, num=100):\n",
    "    \"\"\"计算贝塞尔曲线点\"\"\"\n",
    "    n = len(points) - 1\n",
    "    t = np.linspace(0, 1, num)\n",
    "    curve = np.zeros((num, 2))\n",
    "    \n",
    "    for i in range(n + 1):\n",
    "        binom = math.comb(n, i)  # 二项式系数\n",
    "        term = binom * (1 - t)**(n - i) * t**i\n",
    "        curve += np.outer(term, points[i])\n",
    "    \n",
    "    return curve\n",
    "\n",
    "# 设置控制点\n",
    "points1 = np.array([[0, 0], [1, 1]])  # 一阶(线性)\n",
    "points2 = np.array([[0, 0], [0.5, 1], [1, 0]])  # 二阶(二次)\n",
    "points3 = np.array([[0, 0], [0.3, 1], [0.7, -1], [1, 0]])  # 三阶(三次)\n",
    "\n",
    "# 计算曲线点\n",
    "curve1 = bezier_curve(points1)\n",
    "curve2 = bezier_curve(points2)\n",
    "curve3 = bezier_curve(points3)\n",
    "\n",
    "# 绘制图形\n",
    "plt.figure(figsize=(12, 4))\n",
    "\n",
    "# 一阶贝塞尔曲线\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.plot(points1[:, 0], points1[:, 1], 'ro-', label='控制多边形')\n",
    "plt.plot(curve1[:, 0], curve1[:, 1], 'b-', label='一阶贝塞尔曲线')\n",
    "plt.title('一阶贝塞尔曲线(线性)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.axis('equal')\n",
    "\n",
    "# 二阶贝塞尔曲线\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.plot(points2[:, 0], points2[:, 1], 'ro-', label='控制多边形')\n",
    "plt.plot(curve2[:, 0], curve2[:, 1], 'b-', label='二阶贝塞尔曲线')\n",
    "plt.title('二阶贝塞尔曲线(二次)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.axis('equal')\n",
    "\n",
    "# 三阶贝塞尔曲线\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.plot(points3[:, 0], points3[:, 1], 'ro-', label='控制多边形')\n",
    "plt.plot(curve3[:, 0], curve3[:, 1], 'b-', label='三阶贝塞尔曲线')\n",
    "plt.title('三阶贝塞尔曲线(三次)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.axis('equal')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "284b1bf0",
   "metadata": {},
   "source": [
    "## 多段连续贝塞尔曲线\n",
    "\n",
    "以下是一个Python程序，演示如何绘制由多段连续的三次贝塞尔曲线组成的复杂曲线，并确保曲线之间的平滑连接（C1连续性）：\n",
    "\n",
    "### Python代码实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9be73fc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.path import Path\n",
    "import matplotlib.patches as patches\n",
    "\n",
    "def cubic_bezier(p0, p1, p2, p3, num=100):\n",
    "\t\"\"\"计算单段三次贝塞尔曲线\"\"\"\n",
    "\tt = np.linspace(0, 1, num).reshape(-1, 1)\n",
    "\tcurve = (1-t)**3 * p0 + 3*(1-t)**2*t * p1 + 3*(1-t)*t**2 * p2 + t**3 * p3\n",
    "\treturn curve\n",
    "\n",
    "# 定义多段贝塞尔曲线的控制点（每段4个点，且保证连续性）\n",
    "control_points = [\n",
    "\t# 第一段曲线\n",
    "\tnp.array([[0, 0], [1, 3], [2, -1], [3, 2]]),\n",
    "\t# 第二段曲线（终点=下一段起点，控制点满足C1连续）\n",
    "\tnp.array([[3, 2], [4, 5], [5, 0], [6, 3]]),\n",
    "\t# 第三段曲线\n",
    "\tnp.array([[6, 3], [7, 1], [8, 4], [9, 0]])\n",
    "]\n",
    "\n",
    "# 计算所有曲线段\n",
    "curves = []\n",
    "for segment in control_points:\n",
    "\tcurve = cubic_bezier(segment[0], segment[1], segment[2], segment[3])\n",
    "\tcurves.append(curve)\n",
    "\n",
    "# 绘制图形\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# 绘制曲线\n",
    "colors = ['blue', 'green', 'red']\n",
    "for i, (curve, segment) in enumerate(zip(curves, control_points)):\n",
    "\t# 绘制曲线段\n",
    "\tplt.plot(curve[:, 0], curve[:, 1], color=colors[i], \n",
    "\t\t\t\t\t\tlabel=f'Segment {i+1}', linewidth=2.5)\n",
    "\t\n",
    "\t# 绘制控制点和控制线\n",
    "\tplt.plot(segment[:, 0], segment[:, 1], 'o--', \n",
    "\t\t\t\t\t\tcolor=colors[i], alpha=0.3, linewidth=1)\n",
    "\t\n",
    "\t# 标记控制点\n",
    "\tfor j, point in enumerate(segment):\n",
    "\t\t\tplt.text(point[0], point[1], f'P{i}{j}', fontsize=8,\n",
    "\t\t\t\t\t\t\t\tha='right' if j%2 else 'left', va='bottom')\n",
    "\n",
    "# 标记连接点（确保连续性）\n",
    "for i in range(len(control_points)-1):\n",
    "\tp = control_points[i][3]  # 上一段的终点\n",
    "\tplt.plot(p[0], p[1], 'ko', markersize=8)\n",
    "\tplt.text(p[0], p[1], f' Joint {i+1}', fontsize=10, va='center')\n",
    "\n",
    "plt.title('Multi-segment Cubic Bézier Curves with C1 Continuity')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.axis('equal')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3f6e360",
   "metadata": {},
   "source": [
    "### 关键说明\n",
    "\n",
    "#### 1. 连续性保证\n",
    "- **C0连续**  \n",
    "  每段的终点是下一段的起点（如 `P03 = P10`）\n",
    "  \n",
    "- **C1连续**  \n",
    "  连接点两侧的控制点共线且等距（`P02-P03 = P10-P11`）\n",
    "\n",
    "#### 2. 控制点设计\n",
    "- 每段曲线需要4个控制点\n",
    "- 相邻段的共享控制点确保连续性\n",
    "  ```python\n",
    "  # 示例控制点定义\n",
    "  control_points = [\n",
    "      [P00, P01, P02, P03],  # 第一段\n",
    "      [P10, P11, P12, P13],  # 第二段（P10 = P03）\n",
    "      ...\n",
    "  ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ba166155",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "当x=1.5时，y=1.0000\n",
      "\n",
      "多个点的计算结果:\n",
      "x=0.00, y=0.0000\n",
      "x=0.33, y=0.7599\n",
      "x=0.67, y=1.1166\n",
      "x=1.00, y=1.1852\n",
      "x=1.33, y=1.0809\n",
      "x=1.67, y=0.9191\n",
      "x=2.00, y=0.8148\n",
      "x=2.33, y=0.8834\n",
      "x=2.67, y=1.2401\n",
      "x=3.00, y=2.0000\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def cubic_bezier_y(control_points, x):\n",
    "    \"\"\"\n",
    "    计算三次贝塞尔曲线上给定x坐标对应的y值\n",
    "    \n",
    "    参数:\n",
    "        control_points: 四个控制点的列表/数组，格式为 [[x0,y0], [x1,y1], [x2,y2], [x3,y3]]\n",
    "        x: 要计算的x坐标（可以是标量或数组）\n",
    "        \n",
    "    返回:\n",
    "        对应的y坐标值\n",
    "    \"\"\"\n",
    "    # 解包控制点\n",
    "    P0, P1, P2, P3 = np.array(control_points)\n",
    "    \n",
    "    # 定义三次贝塞尔曲线的参数方程\n",
    "    def x_t(t):\n",
    "        return (1-t)**3 * P0[0] + 3*(1-t)**2*t * P1[0] + 3*(1-t)*t**2 * P2[0] + t**3 * P3[0]\n",
    "    \n",
    "    def y_t(t):\n",
    "        return (1-t)**3 * P0[1] + 3*(1-t)**2*t * P1[1] + 3*(1-t)*t**2 * P2[1] + t**3 * P3[1]\n",
    "    \n",
    "    # 对于给定的x，求解对应的t值\n",
    "    def find_t_for_x(x_val):\n",
    "        # 使用牛顿迭代法求解t值\n",
    "        t = 0.5  # 初始猜测\n",
    "        for _ in range(20):  # 最多迭代20次\n",
    "            f = x_t(t) - x_val\n",
    "            if abs(f) < 1e-6:\n",
    "                return t\n",
    "            # 计算导数\n",
    "            df = (-3*(1-t)**2 * P0[0] \n",
    "                  + 3*(1-t)*(1-3*t) * P1[0] \n",
    "                  + 3*t*(2-3*t) * P2[0] \n",
    "                  + 3*t**2 * P3[0])\n",
    "            t = t - f/df\n",
    "            t = np.clip(t, 0, 1)  # 保证t在[0,1]范围内\n",
    "        return t\n",
    "    \n",
    "    # 处理标量或数组输入\n",
    "    if isinstance(x, (list, np.ndarray)):\n",
    "        t_values = [find_t_for_x(xi) for xi in x]\n",
    "        return np.array([y_t(t) for t in t_values])\n",
    "    else:\n",
    "        t = find_t_for_x(x)\n",
    "        return y_t(t)\n",
    "\n",
    "\n",
    "# 示例用法\n",
    "if __name__ == \"__main__\":\n",
    "    # 定义控制点\n",
    "    control_points = [[0, 0], [1, 3], [2, -1], [3, 2]]\n",
    "    \n",
    "    # 计算单个x值\n",
    "    x = 1.5\n",
    "    y = cubic_bezier_y(control_points, x)\n",
    "    print(f\"当x={x}时，y={y:.4f}\")\n",
    "    \n",
    "    # 计算多个x值\n",
    "    x_values = np.linspace(0, 3, 10)\n",
    "    y_values = cubic_bezier_y(control_points, x_values)\n",
    "    print(\"\\n多个点的计算结果:\")\n",
    "    for x, y in zip(x_values, y_values):\n",
    "        print(f\"x={x:.2f}, y={y:.4f}\")\n",
    "    \n",
    "    # 可视化\n",
    "    import matplotlib.pyplot as plt\n",
    "    t = np.linspace(0, 1, 100)\n",
    "    curve_x = (1-t)**3 * control_points[0][0] + 3*(1-t)**2*t * control_points[1][0] + 3*(1-t)*t**2 * control_points[2][0] + t**3 * control_points[3][0]\n",
    "    curve_y = (1-t)**3 * control_points[0][1] + 3*(1-t)**2*t * control_points[1][1] + 3*(1-t)*t**2 * control_points[2][1] + t**3 * control_points[3][1]\n",
    "    \n",
    "    plt.figure(figsize=(8, 6))\n",
    "    plt.plot(curve_x, curve_y, 'b-', label='贝塞尔曲线')\n",
    "    plt.plot([p[0] for p in control_points], [p[1] for p in control_points], 'ro--', label='控制点')\n",
    "    plt.scatter(x_values, y_values, c='g', s=100, label='计算点')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.title('三次贝塞尔曲线示例')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
